We examine particle production from spherical bodies collapsing into extremal Reissner-Nordström black holes. Kruskal coordinates become ill defined in the extremal case, but we are able to find a simple generalization of them that is good in this limit. The extension allows us to calculate the late-time world line of the center of the collapsing star, thus establishing a correspondence with a uniformly accelerated mirror in Minkowski spacetime. The spectrum of created particles associated with such uniform acceleration is nonthermal, indicating that a temperature is not defined. Moreover, the spectrum contains a constant that depends on the history of the collapsing object. At first sight this points to a violation of the no-hair theorems; however, the expectation value of the stress-energy-momentum tensor is zero and its variance vanishes as a power law at late times. Hence, both the no-hair theorems and the cosmic censorship conjecture are preserved. The power-law decay of the variance is in distinction to the exponential falloff of a nonextremal black hole. Therefore, although the vanishing of the stress tensor’s expectation value is consistent with a thermal state at zero temperature, the incipient black hole does not behave as a thermal object at any time and cannot be regarded as the thermodynamic limit of a nonextremal black hole, regardless of the fact that the final product of collapse is quiescent.

Nonthermal nature of incipient extremal black holes

SONEGO, Sebastiano
2000

Abstract

We examine particle production from spherical bodies collapsing into extremal Reissner-Nordström black holes. Kruskal coordinates become ill defined in the extremal case, but we are able to find a simple generalization of them that is good in this limit. The extension allows us to calculate the late-time world line of the center of the collapsing star, thus establishing a correspondence with a uniformly accelerated mirror in Minkowski spacetime. The spectrum of created particles associated with such uniform acceleration is nonthermal, indicating that a temperature is not defined. Moreover, the spectrum contains a constant that depends on the history of the collapsing object. At first sight this points to a violation of the no-hair theorems; however, the expectation value of the stress-energy-momentum tensor is zero and its variance vanishes as a power law at late times. Hence, both the no-hair theorems and the cosmic censorship conjecture are preserved. The power-law decay of the variance is in distinction to the exponential falloff of a nonextremal black hole. Therefore, although the vanishing of the stress tensor’s expectation value is consistent with a thermal state at zero temperature, the incipient black hole does not behave as a thermal object at any time and cannot be regarded as the thermodynamic limit of a nonextremal black hole, regardless of the fact that the final product of collapse is quiescent.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/686919
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